Question

The following table shows (hypothesized) opinions voiced by two different age groups in Scotland, in response to an opinion poll on the recent referendum for Scottish independence from the U.K. Do the two Age groups differ significantly (in a statistical sense), in terms of the proportions favoring the status quo (i.e., NO to Scottish independence)? Perform a suitable statistical test to support your answer.

Age Group	Sample Size	Do NOT want Scottish independence from the U.K.
Under 30	100	48
30 - 49	150	78

use excel

Answer 1

Result:

The following table shows (hypothesized) opinions voiced by two different age groups in Scotland, in response to an opinion poll on the recent referendum for Scottish independence from the U.K. Do the two Age groups differ significantly (in a statistical sense), in terms of the proportions favoring the status quo (i.e., NO to Scottish independence)? Perform a suitable statistical test to support your answer.

Age Group	Sample Size	Do NOT want Scottish independence from the U.K.
Under 30	100	48
30 - 49	150	78

Two sample proportion test

Ho: P₁ = P₂   H₁: P₁ ≠ P₂

p1=48/100=0.48

p2=78/150=0.52

P = (x1+x2)/(n1+n2)

=(48+78)/(100+150)=0.504

= -0.6197

Table value of z at 0.05 level = 1.96

Rejection Region: Reject Ho if z < -1.96 or z > 1.96

Calculated z = -0.6197 not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to conclude that proportions favoring the status quo for the two Age groups differ significantly.

Excel Addon PHStat used

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	48
Sample Size	100
Group 2
Number of Items of Interest	78
Sample Size	150
Intermediate Calculations
Group 1 Proportion	0.48
Group 2 Proportion	0.52
Difference in Two Proportions	-0.04
Average Proportion	0.5040
Z Test Statistic	-0.6197
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.5355
Do not reject the null hypothesis